Most Aztecs were actually defeated by disease, not war. It can be easily said that if not for the smallpox contracted from the Europeans that wiped out so many of them, especially their leaders, that it is extremely unlikely they would have fallen to the Spanish. The amount of harm caused by European diseases was tremendous, it is estimated that over twenty million Mexicans died in a period of just five years due to the diseases brought over by the Spanish.
They didn't take Latin America all in one sweep. Individual mercenary forces slowly took it. Cortés and his Indian assistance fought the Aztecs. Moctezuma was killed, and soon all of Mexico was under Spanish control. Pizarro soon tried for Cuzco, and it fell in 1533. The Spanish build Lima, their capital in Peru. They explored Chile and the American Southwest. In 1570, there were 192 Spanish settlements on the new continent.
The Political life of Aztecs: The Great Speaker, or the Emperor, of the Aztec Empire gives rules people must obey, however he can be dismissed. He is the most wealthiest and powerful person in the empire. The son of the Ruler isn't necessarily the next ruler, the Councils of Wise Men chooses the next ruler.